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Homework Help: Particle in a box problem

  1. Aug 29, 2010 #1
    Hi, I have been given the following problem;

    If an electron is confined to a 1-D potential well of infinite barrier height and width
    L, the normalized wavefunction Psi(x) of the electron in the various quantized states, n,
    is given as Psin(x)=(2/L)0.5 sin(n pi x / L).

    For the n=2 state, what is the probability of finding the electron at the centre of the
    well?


    I have calculated these probability questions in the past, but they have always been for a probability across a range of values for x, i.e from 0 to L/2, which I use as my limits when integrating. In this case however, it is asking about a specific point. I assume that the answer is zero, as the upper and lower limit are identical. Is this correct?

    Thanks.
     
  2. jcsd
  3. Aug 29, 2010 #2

    vela

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    Yes, with a continuous probability distribution, the probability of a obtaining a specific number is always 0. It's only meaningful to talk about the probability of finding the random variable in some range of values.

    I think it was just a poorly worded question. The problem likely wants you to find the probability of finding the particle between x=L/2 and x=L/2+dx.
     
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